In this section, we introduce the notion of walk-tree. Walk-trees are topological constructions which
are defined with respect to the graph \(G=(V,E)\)  and a set of walks \({\mathcal {P}}\)  in this graph.
This notion generalises constructions from the algebraic graph theory and elsewhere such as the
tree of self-avoiding walks, or the path-trees (introduced by Godsil, e.g., see
[1]}), or the universal cover (e.g. see [2]}) etc.
